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Fortschritte der Physik

Parametric down‐conversion experiments with stationary fields

Vlasta Peřinová, A. Lukš

Published Feb 26, 2003• 2 citations
Publisher

Abstract

Abstract Returning from the Wigner to the Hilbert‐space formalism, we have augmented the detailed analysis of the four experiments by Casado et al. [Phys. Rev. A55, 3879 (1997)]. Starting from realistic, though arbitrary, parameters we have made numerical calculations of the visibility of fourth‐order interference. We have found that two of these experiments are rather proposals than reported ones and we have formulated an alternative to the description of one of them.

DOI
10.1002/prop.200310029

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Wigner-PDC description of photon entanglement can still be made completely local

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Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward subtraction of the average ZPF intensity at the Wigner image of the detection process.

•Nov 16, 2011•0 citations
Abstract Returning from the Wigner to the Hilbert‐space formalism, we have augmented the detailed analysis of the four experiments by Casado et al. [Phys. Rev. A55, 3879 (1997)]. Starting from realistic, though arbitrary, parameters we have made numerical calculations of the visibility of fourth‐order interference. We have found that two of these experiments are rather proposals than reported ones and we have formulated an alternative to the description of one of them.
In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments [Phys. Rev. Lett. 62, 2205 (1989)], Rarity and Tapster's experiments [Phys. Rev. Lett. 64, 2495 (1990)], and induced coherence without induced emission [X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 67, 318 (1991)].
The Wigner representation is developed in the Heisenberg picture for the study of experiments involving photon pairs created in the process of parametric down conversion. After the general description of a light beam and the theory of detection (restricted here to single count probabilities in the Wigner formalism) the theory of parametric downconversion is developed to the point of calculating the autocorrelations of the signal and idler beams. Two recent experiments are analyzed in detail: frustrated two-photon creation by interference, and induced coherence and indistinguishability.
We explore semiclassical and quantum descriptions of fourth-order interference that are built upon classical and quantum Gaussian-state models for the signal and idler outputs from a parametric down converter. Our approach unifies the analysis of fourth-order interference with those for squeezing and photon twins. It also demonstrates that a purely-quantum fourth-order interference effect can be claimed at fringe visibilities substantially below the commonly accepted threshold of 50%. We start with a pair of models - one quantum and one classical - for the signal and idler fields produced by parametric down conversion.>
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward subtraction of the average ZPF intensity at the Wigner image of the detection process.